Signature
PV = A * (1 - (1+r)^(-n)) * (1+r) / r
| Inputs | Definition | Unit |
|---|---|---|
A | Instalment paid at the start of each year, set by HE-FM-AP-001 or by the contract | currency per instalment |
r | Annual discount rate for costs in the economic evaluation, as a decimal, for example 0.035 in the NICE reference case. Above zero; at zero the present value is n times A | rate per year |
n | Number of yearly instalments, including the payment at treatment | count |
PV | Present value at the date of treatment of the n fixed instalments, discounted at the evaluation discount rate | currency |
|---|
Function
Annuity payment schedule valuation function
Turns the upfront price of a one-off therapy into equal yearly instalments at an agreed financing rate, and values the resulting schedule, fixed or conditional on continued response, at the discount rate of the economic evaluation. The instalment is set so that the schedule matches the upfront price at the financing rate. The cost that enters a cost-effectiveness model is the present value of the expected payments at the evaluation's own rate, not the list price or the nominal sum of the instalments.
Try this function
Implementations
Excel
Present value of fixed instalments with Excel PV
Excel PV with a type argument of 1 discounts payments made at the start of each period. The instalment is entered as a negative payment so that the present value is returned as a positive amount.
=PV(DiscRate,NInstal,-Instalment,0,1)
Assumptions
Every fixed annuity instalment is paid
Every instalment falls due once the patient is treated, whatever happens to the benefit, as in a fixed annuity. When later payments depend on continued response, the expected present value HE-FM-AP-003 applies instead.
Yearly discounting of instalments from the date of treatment
Year 0 is the date of treatment and its payment is not discounted, and later payments are discounted once a year at a constant rate r. The NICE manual (PMG36) sets 3.5% a year for costs and health effects in the reference case.
Worked examples
Five £219,976 instalments discounted at 3.5%
Five instalments of £219,976 discounted at 3.5% have a present value of about £1,027,965, about 2.8% more than the £1 million upfront price, because the 5% financing rate exceeds the evaluation rate. The article's £1,027,948 uses discount factors rounded to four decimal places.
A = 219976; r = 0.035; n = 5; PV = 1027965
Interest-free split of a £1 million therapy over five years
Five payments of £200,000 with no financing charge have a present value at 3.5% of about £934,616, about 6.5% below the upfront price, so the split works as a hidden price reduction.
A = 200000; r = 0.035; n = 5; PV = 934616
Common errors
Nominal instalment total entered as the therapy cost
Entering the nominal total of £1,099,880 in the £1 million example instead of the present value of about £1,027,965 overstates the cost by about 7%, and the gap grows with the length of the schedule and the discount rate.
Instalment schedule discounted at the financing rate
Discounting the instalments at the financing rate always returns the upfront price, so the financing charge disappears from the model. The schedule has to be valued at the evaluation's own rate, which in the £1 million example gives about £1,027,965 rather than £1,000,000.
Sources
Discounting annuity-based payments at a social discount rate
Van Dyck W, Michelsen S, Veredas D, Huys I, Luyten J, Simoens S. When do annuity-based payments help to address the affordability challenge of funding advanced therapies? Insights from a budget impact simulation. Journal of Market Access and Health Policy. 2026;14(2):23. Section 3.1.2, equation 2, which discounts the budget impact of annuity-based payments at a social discount rate r so that it can be compared with upfront payment.
NICE reference-case discount rate for valuing instalment schedules
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated March 2026. Section 4.5.1, which discounts costs and health effects at the same rate of 3.5% a year in the reference case, and section 4.5.3 on the 1.5% rate.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0